Five-Minute Check (over Lesson 6–3)
CCSS
Then/Now
New Vocabulary
Key Concept: Definition of nth Root
Key Concept: Real nth Roots
Example 1: Find Roots
Example 2: Simplify Using Absolute Value
Example 3: Real-World Example: Approximate Radicals
Over Lesson 6–3
A.
B.
C.
D. D = {x | x ≤ –2}, R = {y | y ≥ 0}
Over Lesson 6–3
A.
B.
C.
D.
Over Lesson 6–3
A.
B.
C.
D.
Over Lesson 6–3
A.
C.
B.
D.
Over Lesson 6–3
A.
C.
B.
D.
Over Lesson 6–3
The point (3, 6) lies on the graph of
Which ordered pair lies on the graph of
A.
B.
C. (2, –2)
D. (–2, 2)
Content Standards
A.SSE.2 Use the structure of an expression
to identify ways to rewrite it.
Mathematical Practices
6 Attend to precision.
You worked with square root functions.
• Simplify radicals.
• Use a calculator to approximate radicals.
• nth root
• radical sign
• index
• radicand
• principal root
Find Roots
= ±4x4
Answer: The square roots of 16x8 are ±4x4.
Find Roots
Answer: The opposite of the principal square root of
(q3 + 5)4 is –(q3 + 5)2.
Find Roots
Answer:
Find Roots
Answer:
A. Simplify
A. ±3x6
B. ±3x4
C. 3x4
D. ±3x2
.
B. Simplify
A. –(a3 + 2)4
B.
–(a3 + 2)8
C. (a3 + 2)4
D. (a + 2)4
.
C. Simplify
A. 2xy2
B. ±2xy2
C. 2y5
D. 2xy
.
D. Simplify
A. –4
B. ±4
C. –2
D. ±4i
.
Simplify Using Absolute Value
Note that t is a sixth root of t 6. The index is even, so the
principal root is nonnegative. Since t could be negative,
you must take the absolute value of t to identify the
principal root.
Answer:
Simplify Using Absolute Value
Since the index is odd, you do not need absolute value.
Answer:
A. Simplify
A. x
B. –x
C. |x|
D. 1
.
B. Simplify
A. |3(x + 2)3|
B. 3(x + 2)3
C. |3(x + 2)6|
D. 3(x + 2)6
.
Approximate Radicals
A. SPACE Designers must create satellites that
can resist damage from being struck by small
particles of dust and rocks. A study showed that
the diameter in millimeters d of the hole created in
a solar cell by a dust particle traveling with energy
k in joules is about
Estimate
the diameter of a hole created by a particle
traveling with energy 3.5 joules.
Understand
You are given the value for k.
Plan
Substitute the value for k into the
formula. Use a calculator to evaluate.
Approximate Radicals
Solve
Original formula
k = 3.5
Use a calculator.
Answer: The hole created by a particle traveling with
energy of 3.5 joules will have a diameter of
approximately 1.237 millimeters.
Approximate Radicals
Check
Original equation
Add 0.169 to each
side.
Divide both sides by
0.926.
Cube both sides.
Simplify.
Approximate Radicals
B. SPACE Designers must create satellites that
can resist damage from being struck by small
particles of dust and rocks. A study showed that
the diameter in millimeters d of the hole created in
a solar cell by a dust particle traveling with energy
k in joules is about
If a hole
has diameter of 2.5 millimeters, estimate the
energy with which the particle that made the hole
was traveling.
Approximate Radicals
Solve
Original formula
d = 2.5
Use a calculator.
Answer: The hole with a diameter of 2.5 millimeters
was created by a particle traveling with
energy of 23.9 joules.
A. PHYSICS The time T in seconds that it takes a
pendulum to make a complete swing back and forth
is given by the formula
where L is the
length of the pendulum in feet and g is the
acceleration due to gravity, 32 feet per second
squared. Find the value of T for a 2-foot-long
pendulum.
A. about 0.25 second
B. about 1.57 seconds
C. about 12.57 seconds
D. about 25.13 seconds
B. PHYSICS The time T in seconds that it takes a
pendulum to make a complete swing back and forth
is given by the formula
where L is the
length of the pendulum in feet and g is the
acceleration due to gravity, 32 feet per second
squared. How long is the pendulum if it takes 5
seconds to swing back and forth?
A. about 2.5 feet
B. about 10 feet
C. about 20.3 feet
D. about 25.5 feet